Research

Research interest: My primary research interests are in analysis and partial differential equations, with a particular focus on the dynamics of the two-dimensional Euler equations and advection-diffusion equations.

Preprint

#1 Exponential lower bounds for the advection-diffusion equation with shear flows, Yupei Huang and Xiaoqian Xu.  arXiv preprint:   arXiv:2511.14512 

#2 On the flexibility of 2D Euler steady states,Tarek, Elgindi and Yupei Huang. arXiv preprint:   arXiv:2604.12962

Publication

#1 Formation of singularity for the classical solutions of the rotating shallow water system. Yupei Huang and Chunjing Xie. Journal of Differential Equations 348 (2023): 45-65.

#2 Regular and singular steady states of 2D incompressible Euler equations near the Bahouri-Chemin patch. Tarek, Elgindi and Yupei Huang. Archive for Rational Mechanics and Analysis 249 (1), 1-31

#3 On the rigidity of uniformly rotating vortex patch near the Rankine vortex   Yupei Huang. Nonlinearity(2025)

#4 H{ö}lder convergence of singular steady states to Bahouri-Chemin patch  Yupei Huang and Chilin Zhang.  Calculus of Variations and Partial Differential Equations 64 (6), 1-31

#5 A Classification theorem for steady Euler flows Tarek M. Elgindi, Yupei Huang, Ayman R. Said and Chunjing Xie. To appear in Duke Mathematical Journal